Statistical thinking in Medicine (Historical Overview)

This is a talk I gave during the third year of my Residency in Internal Medicine at the University of Cincinnati. It goes over the history and evolution of statistical concepts underlying Medical
…

This is a talk I gave during the third year of my Residency in Internal Medicine at the University of Cincinnati. It goes over the history and evolution of statistical concepts underlying Medical Science and Evidence Based Medicine

A nice summary (from which most of the material after Laplace's time came from) is given in:
http://www.worldscibooks.com/etextbook/4854/4854_chap1.pdf

“ Prove thy servants, I beseech thee, ten days ; and let them give us pulse to eat, and water to drink.

Then let our countenances be looked upon before thee, and the countenance of the children that eat of the portion of the king’s meat: and as thou seest,deal with thy servants.

So he consented to them in this matter, and proved them ten days. And at the end of ten days their counte-nances appeared fairer and fatter in flesh than all the children which did eat the portion of the king’s meat.

Thus Melzar took away the portion of their meat, and the wine that they should drink and gave them pulse.

Quality Control questions about the Study:

Was there a stopping rule?

Why ten days?

What was the outcome measured (“fairness”)

Was there a discrete or continuous scale employed?

How were the inferences summarized?

Daniel may not be Fisher but

Use of experimental evidence to settle a (health-related) issue

Control group was employed (with similar characteristics?)

The evidence was used to change state policy and Daniel and his companions were allowed to continue their cosher diet

14.
Probabilistic Ideas in Galen’s work I How can we assert that the empirical weight of evidence points towards a particular cause of a disease or an efficacious treatment? “ I assert that experience has shown that what has produced a like result in three cases can produce the reverse in three others. I say that a thing seen may be seen exactly as before, and yet belong to those things which are of both kinds, or to those things that happen often or to those things that take place but rarely. […] What is to prevent the medicine that is being tested from having a given effect on two hundred people and the reverse effect on twenty others ; and to prevent that of the first six people who were seen at first and on whom the remedy took effect, three belong to the two hundred and three to the twenty, without you being able to know which three belong to the two hundred and which to the twenty, even if you were a soothsayer? … Therefore I say of what has been seen but once , that it is not technical, just as the single grain of wheat is not a perfect heap; but if it is a thing that is seen many times in the same way , then I call it technical…”

Can one use finite number of observations to add to the weight of evidence?

18 centuries before the work of Kiaer who stated that “the part (sample) can replace the whole (population)” a physician described the formal foundation of sample based inference and the need for representativeness

Can one use finite number of observations to add to the weight of evidence?

“ Having learnt in advance from the works of nature you have already seen, you should hope that its art concerning all other [creatures] is the same. In the same way we form an opinion about the arts of people, because we do not expect to see all the statues that Phidias and Polycleitus had made, but from the ones we have seen, we hope the others [are the same], accordingly, the one who gained experience [in selecting] the works of nature, can conclude about [any other] from what he has already seen” Galen. De anatomicis administrationibus libri ix. In: Kühn CG. Claudii Galeni opera omnia , volume 2. Olms, Hildelsheim: 1964:545 pp. line 11-17.

Can one use finite number of observations to add to the weight of evidence?

Galen. De sanitate tuenda libri vi. In Kuhn Corpus medicorum Graecorum, Koch K., Leipzig, 1923 vol. 6, p. 212, line 1 to p. 214, line 5. “ Theon (a contemporary gymnast) made a mistake by saying that hot baths are of great beneficence to all people, because Theon used hot baths after hard workouts. But he [made his observations] only on good athletes in very good shape who had hot baths after hard workouts and benefited from them “

18.
Statistical Ideas in Galen’s work III Extrapolating from a small group of cases can be dangerous “ […] But if it happened once in every three or four successful deliveries that the fetus be prevented [to exit the uterus because of its wrong position], it follows that in every four hundred fetuses one hundred will be prevented. But ... this is seen to happen once in multiple thousands ... ” Galen. De usu partium. In: Helmreich G.. Galeni de usu partium libri xvii . Hakkert, Amsterdam: 1968; volume 4, page 248, line 4-17.

“ Let n denote the number of people in the sample studied, p the proportion of the sample possessing the characteristic under study, and P the underlying (but unknown) proportion who possess the characteristic. Inferences about P may be made using the binomial probability distribution …. A confidence interval may be assigned to the underlying proportion”

highlight the significance of an experiment’s result repeatability in order to arrive at a reliable scientific conclusion

(“.. you must deny me faith in my words .. I transfer the authority to anyone who wishes, to come and show me if what I say concerning the findings of anatomies is really true. For I have already shown thousands of times … And this must be shown by anyone after I and my pupils have died “)

Understood that the definition of health v.s. disease is not always clear, and a quantitative definition might be required

“ So, what is the concept of a healthy body construction, and what of a diseased? The healthy one has all its systems functioning; the diseased, not functioning. But if someone who is healthy has his systems not functioning so well as someone else's, but not malfunctioning, he is said to have a bad constitution , not a disease. … So, it is necessary to define what is the amplitude of health, since there are many many differences between healthy bodies on its [health’s] upper and lower limits . “

Provide the first statistical description of a medical object (i.e. the expected day of delivery)

“ For the seven month births I transfer my whole life's knowledge as I always very carefully acquainted the exact time of the conception of the sperm by women, which time if you ignore it is impossible to find the date of birth. And I found most of them between 190 and 200 days , a few of them some days earlier or some days later , but none before day 184 or after day 204 .”

method by which we might judge concerning the probability that an event has to happen, in given circumstances, upon supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain other number of times.

These formulas are behind the clinical use of the PIOPED study data and the dreaded question by Nuclear Medicine physicians: “What’s your pre-test probability doc?”

Clinical use of any laboratory test can (and should) be guided by the interplay of test – characteristics (objectively quantifiable as sensitivity, specificity) and a subjective judgment (pre-test probability)

Precision to be sought after is the 99.5% favoring the new treatment versus the standard (the posterior Probability favoring Lithotrity was <0.0001)

Used the same argument to criticize the small number of observations in Louis studies on pneumonia, TB and typhoid

In Germany, the ophthalmologist Julius Hirschberg (1843–1925), concerned about the number of observations required by Gavarret’s assumption of 212:1 odds, modified the formula by using a lower standard of confidence of 11:1 or 91.6%.

Eventually the standard would rise to the 95%, a number that would attain religious belief status

Joseph Lister (1827–1912) publishe s his pioneering work with antiseptic surgery in 1870

A verage mortality rate was 45.7% (16/35) for all surgical procedures performed at the University of Edinburgh in the years 1864–1866

Reports that it was 15% (6/40) for all surgical procedures performed in the three-year period 1867–1869.

Although he used this statistical result to show the efficacy of the new antiseptic method, he claimed that the science behind this was the germ theory of disease as proposed by Louis Pasteur (1822–1895) and not the numbers!

47.
Statistical Developments of the late 19 th Century – Early 20 th Century

Heavily influenced by Karl Pearson, who similarly to Louis would try to “spread the word” through his students. They would go to subsequently establish the first statistic departments in Medical/Public Health Schools

Fisher, R. A. (1958). Statistical Methods for Research Workers, 13th edn.,Hafner, New York. “ To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of”

“ Four of the 55 S patients (7%) and 14 of the 52 C patients (27%) died before the end of six months. The difference between the two series is statistically significant; the probability of it occurring by chance is less than one in a hundred ”

Statistical Ideas and Applications in Medicine are not the invention of the 20 th century

Physicians entertained the idea that medical knowledge can be understood in quantitative terms thousands of years ago

However there has always been a significant resistance in accepting the idea, in spite of its effectiveness in practice (i.e. The limits of evidence-based medicine. R espir Care. 2001 Dec;46(12):1435-4 for a modern version of the same arguments)